When do you stop the iterations?
The iterations stop, i.e., convergence is achieved, when the
data residuals, on average, are at about the same level as the
estimated noise. Otherwise you are fitting
noise to the model. It is our experience that with proper smoothing
no more than 10-30 iterations are needed for convergence.

How do you estimate the average data residual? A quick and dirty method
is to simply pick the data and estimate it from your subjective picking
intuition. Another quick and dirty
way is to say that the pick error is about the T/4where T is the dominant period of the wavelet.

How do you know if you have converged to the correct or unique model?
The iterative solution may get stuck in a local minimum, so that
the reconstructed model is incorrect even though the traveltime
residuals are small. To check for uniqueness you can construct
a set of completely different starting models, and see if they
all lead to the same final model. If so, then your confidence about
arriving at a unique model is increased (but not guaranteed).